The veteran defensive end was openly frustrated with his own play last season. Tuck recorded just four sacks, his lowest total since an injury-shortened 2006 season, and said he looked like a different player when he watched himself on film.

"Obviously, Justin hasn’t played as well as we think he can play and what kind of player he has shown to be in the past," Reese said. "And he knows that. Justin and I recently had a really long conversation and talked about some of those things, and he really wants to get back to the old Justin Tuck and be the player that we know him to be."

The defense as a whole had a disappointing year, finishing 31st in the league and giving up a franchise-high 6,134 yards of offense to opponents, a contributing factor as the Giants finished 9-7 and missed the playoffs.

Tuck was one of many players whose production was down, which in turn he said caused him to make mistakes.

"I pressed," Tuck said earlier this month while in New Orleans during Super Bowl week. "I could just tell I was not allowing the game to come to me, trying to make plays when really, there wasn’t plays to be made. I know that sounds funny, but sometimes in plays, in certain calls and certain plays, your job is to make sure that nothing bad happens. It isn’t for you to have a sack or cause a fumble, whatever it may be. "

Tuck said his objective this offseason is to work with the coaching staff to "get ahead of the curve," and make sure opponents can't attack the defensive line in the same ways that worked last season.

And the purpose of meeting with Reese was discussing getting Tuck back to his Pro Bowl and Super Bowl champion form.

"Hopefully he can get healthy and have a good offseason and get back to his old form," Reese said.

It is "not correct" that Hakeem Nicks is a priority over fellow receiver Victor Cruz, Reese said, echoing what co-owner John Mara said earlier this week. An ESPN report said that the Giants have prioritized a long-term deal for Nicks over Cruz.

"They’re both good players, we like them both, and I don’t think we like one more than the other," Reese said. "I think they’re both really good football players."

Asked if it is possible to keep both young receivers long-term, Reese said, "I don’t know; we’ll see."

Reese said there is "nothing to report" on the status of contract negotiations with Cruz. The third-year receiver will be a restricted free agent, and Reese said all options are open in terms of potentially using a restricted free agent tender.

There have been "some conversation" about re-signing free-agent left tackle Will Beatty, but no profess to report yet, Reese said.

CB Corey Webster ($9.8 million) and RT David Diehl ($6.9 million) have high cap figures for 2013, so they could be candidates for pay cuts or being cut. Reese had no comment when asked if he's approached them about reworking their contracts or if they'll be back next year.

"It’s a long time before we play in September. I wouldn’t doubt if there’s more changes," Reese said. He said the Giants are in "pretty good position" cap-wise right now.

The door is not closed on a return for DE Osi Umenyiora, Reese said.

"We keep all our options open," Reese said.

Another free agent defensive end, ex-Colt Dwight Freeney, recently said it would be a "dream" to play for Giants. Reese said, "We investigate everything."

Nicks, C David Baas and RG Chris Snee, who each needed offseason surgery, should be ready for training camp, Reese said.

Reese doesn't know if CB Terrell Thomas rushed back from ACL surgery last summer, leading to a third tear of the ligament in his right knee, but he did say "hopefully this time, we’ll take more precaution." Thomas was recently re-signed to a risk-free one-year contract.

The Giants will "continue to look for runners" after Bradshaw's release, Reese said. He confirmed coach Tom Coughlin's plan that the Giants will have a competition at the running back spot between David Wilson, Andre Brown and Da'Rel Scott.